This proposal reflects our continuing efforts in solving problems of measurement error, correlated data and longitudinal/functional (curve) data in general regression settings. With the advancement in technology, data of higher dimension and more complex structures are generated daily. It is a common practice to directly adopt existing procedures that have been applied to data with similar structure to these new studies. Nevertheless, under certain circumstances, this practice could lead to ineffective analyses or even mis-leading conclusions. The investigators of this proposal will put such practice into a framework of measurement error modeling and evaluate its effectiveness and potential drawbacks in term of inducing non-negligible biases. The learned knowledge would allow researchers to develop suitable modeling strategies and new statistical methods that best exploit the information embedded in the data. The proposed research topics have arisen naturally from several important studies. These studies include (i) a long-term longitudinal study with the goal of studying effects of life-long risk exposure on health conditions later in life, (i) nutrition dietary mea- surements and metabolites, measured by multiple-devices, from subjects of diverse backgrounds, (iii) multi-platform genomic datasets, including microRNA, polysomal and total mRNA, collected from the same subjects at the same time for the purpose of investigating colon cancer tumorigenesis, and (iv) a spectroscopic oblique incidence reflectometry skin-lesion diagnostic study. A shared objective behind these research projects is to advance understanding of information embedded in the data and consequently to enhance disease prevention and early detection. The major focus of this proposal remains to be the development of intuitive and practical models as well as efficient and computa- tionally feasible methods without imposing unnecessary parametric assumptions. Through a series of aims, this research project will provide new modeling strategies and statistical methods that (i) utilize both modeling considerations and variable selection technique to identify suitable time period or effective locations where the changes or treatment effects exist; (ii) utilize a new mixture modeling strategy to flexible yet effectively describe distributions of features/variables of sub-populations, (iii) effectively borrow information through seemingly unrelated observations through correlations while maintain interpretability of outcomes, and finally (iv) utilize measurement-error modeling considerations to effectively link disease outcomes to latent features of correlated functional or longitudinal predictors. We expect our efforts on producing new statistical methods and applying them to important biomedical studies shall have significant impact on advancements in biological and medical research.